After Dean accepts the Mark of Cain from Cain himself in season 9, it begins changing him, granting him supernatural powers, ramping up his bloodlust and making him addicted to using the First Blade. When he is killed by Metatron in 9.23 Do You Believe in Miracles?, the Mark resurrects him as a demon, with the additional bonus that he is immune to exorcism as he is not technically possessing his body but is its natural "owner." He is later cured by Sam in 10.03 Soul Survivor though at that point he still possessed the potential to become a demon again as he still had the Mark of Cain. In 10.23 Brother's Keeper Sam, with the help of Crowley, Castiel, and Rowena, removes the Mark from Dean using the Book of the Damned.
The term "Deanmon" was popularized by the CW promo "Deanmon Rises" which aired in September 2014 ahead of season 10.